Autonomous Version of Collatz Conjecture: Freedom of Choice Makes Unsolved Problem Solvable

Abstract

In original Collatz conjecture, you have no choice, for any given natural number, other than to move from 2x to x or, if x is an odd number, from x to 3x + 1. It is an unsolved problem whether you must eventually reach 1, repeating the move. But I proved autonomous version of the conjecture: if you can choose to move from any x ∈ N to 2x or 3x + 1 or vice versa, you always have a way to reach 1. The counterintuitive example of making certain outcomes of formal rules with uncertain outcomes via introducing freedom of choice shows heuristic and educational value of the multidisciplinary approach, linking mathematics, philosophy, and legal theory.